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@article{FPM_2008_14_8_a1, author = {L. A. Bokut and Yuqun Chen and Yu Li}, title = {Gr\"obner--Shirshov bases for {Vinberg--Koszul--Gerstenhaber} right-symmetric algebras}, journal = {Fundamentalʹna\^a i prikladna\^a matematika}, pages = {55--67}, publisher = {mathdoc}, volume = {14}, number = {8}, year = {2008}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/FPM_2008_14_8_a1/} }
TY - JOUR AU - L. A. Bokut AU - Yuqun Chen AU - Yu Li TI - Gr\"obner--Shirshov bases for Vinberg--Koszul--Gerstenhaber right-symmetric algebras JO - Fundamentalʹnaâ i prikladnaâ matematika PY - 2008 SP - 55 EP - 67 VL - 14 IS - 8 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/FPM_2008_14_8_a1/ LA - ru ID - FPM_2008_14_8_a1 ER -
%0 Journal Article %A L. A. Bokut %A Yuqun Chen %A Yu Li %T Gr\"obner--Shirshov bases for Vinberg--Koszul--Gerstenhaber right-symmetric algebras %J Fundamentalʹnaâ i prikladnaâ matematika %D 2008 %P 55-67 %V 14 %N 8 %I mathdoc %U http://geodesic.mathdoc.fr/item/FPM_2008_14_8_a1/ %G ru %F FPM_2008_14_8_a1
L. A. Bokut; Yuqun Chen; Yu Li. Gr\"obner--Shirshov bases for Vinberg--Koszul--Gerstenhaber right-symmetric algebras. Fundamentalʹnaâ i prikladnaâ matematika, Tome 14 (2008) no. 8, pp. 55-67. http://geodesic.mathdoc.fr/item/FPM_2008_14_8_a1/
[1] Bokut L. A., “Nerazreshimost problemy ravenstva dlya algebr Li i podalgebry konechno opredelënnykh algebr Li”, Izv. AN SSSR. Ser. mat., 36:6 (1972), 1173–1219 | MR | Zbl
[2] Bokut L. A., “Vlozheniya v prostye assotsiativnye algebry”, Algebra i logika, 15:2 (1976), 117–142 | MR | Zbl
[3] Bokut L. A., Kolesnikov P. S., “Bazisy Grëbnera–Shirshova: ot zarozhdeniya do nashikh dnei”, Zap. nauch. sem. Sankt-Peterburg. otd-niya Mat. in-ta im. V. A. Steklova RAN, 272, 2000, 26–67 | MR | Zbl
[4] Bokut L. A., Fong Yu., Ke V.-F., Kolesnikov P. S., “Bazisy Grëbnera i Grëbnera–Shirshova v algebre i konformnye algebry”, Fundament. i prikl. mat., 6:3 (2000), 669–706 | MR | Zbl
[5] Vasileva E. A., Mikhalëv A. A., “Svobodnye levo-simmetrichnye superalgebry”, Fundament. i prikl. mat., 2:2 (1996), 611–613 | MR | Zbl
[6] Vinberg E. B., “Odnorodnye konusy”, DAN SSSR, 133 (1960), 9–12 | MR | Zbl
[7] Zhukov A. I., “Polnye sistemy opredelyayuschikh sootnoshenii dlya neassotsiativnykh algebr”, Mat. sb., 27(69):2 (1950), 267–280 | MR | Zbl
[8] Kurosh A. G., “Neassotsiativnye svobodnye algebry i svobodnoe proizvedenie algebr”, Mat. sb., 20(62):2 (1947), 239–262 | MR | Zbl
[9] Mikhalëv A. A., “Metod kompozitsii Shirshova dlya lievykh superalgebr Li (nekommutativnye bazisy Grëbnera)”, Tr. seminara im. I. G. Petrovskogo, 18, 1995, 277–289 | Zbl
[10] Shirshov A. I., Nekotorye problemy teorii neassotsiativnykh kolets i algebr, Dis. $\dots$ kand. fiz.-mat. nauk, M., 1953
[11] Shirshov A. I., “Podalgebry svobodnykh algebr Li”, Mat. sb., 33(75):2 (1953), 441–452 | MR | Zbl
[12] Shirshov A. I., “odalgebry svobodnykh kommutativnykh i svobodnykh antikommutativnykh algebr”, Mat. sb., 34(76):1 (1954), 81–88 | MR | Zbl
[13] Shirshov A. I., “O svobodnykh koltsakh Li”, Mat. sb., 45(87):2 (1958), 113–122 | MR | Zbl
[14] Shirshov A. I., “O bazakh svobodnykh algebr Li”, Algebra i logika, 1:1 (1962), 14–19 | MR | Zbl
[15] Shirshov A. I., “Nekotorye algoritmicheskie voprosy dlya $\varepsilon$-algebr”, Sib. mat. zhurn., 3:1 (1962), 132–137 | Zbl
[16] Shirshov A. I., “Nekotorye algoritmicheskie problemy dlya algebr Li”, Sib. mat. zhurn., 3:2 (1962), 292–296 | Zbl
[17] Aymon M., Grivel P.-P., “Un théorème de Poincaré–Birkhoff–Witt pour les algèbres de Leibniz”, Commun. Algebra, 31 (2003), 527–544 | DOI | MR | Zbl
[18] Bahturin Y. A., Identical Relations in Lie Algebras, VNU Science Press, 1987 | MR | Zbl
[19] Bahturin Y. A., Groups, Rings, Lie and Hopf Algebras, Kluwer Academis, 2003 | MR | Zbl
[20] Bahturin Y. A., Mikhalev A. A., Petrogradsky V. M., Zaicev M. V., Infinite-Dimensional Lie Superalgebras, De Gruyter Exp. Math., 7, Walter de Gruyter, Berlin, 1992 | MR
[21] Bergman G. M., “The diamond lemma for ring theory”, Adv. Math., 29 (1978), 178–218 | DOI | MR
[22] Bokut L. A., “Gröbner–Shirshov bases for braid groups in Artin–Garside generators”, J. Symbolic Comput., 43 (2008), 397–405 | MR | Zbl
[23] Bokut L. A., “Gröbner–Shirshov bases for the braid groups in the Birman–Ko–Lee generators”, J. Algebra, 321 (2009), 361–376 | DOI | MR | Zbl
[24] Bokut L. A., Chainikov V. V., Shum K. P., “Markov and Artin normal form theorem for braid groups”, Commun. Algebra, 35 (2007), 2105–2115 | DOI | MR | Zbl
[25] Bokut L. A., Chen Y., “Gröbner–Shirshov bases: Some new results”, Proc. of the Second Int. Congress in Algebra and Combinatorics, World Scientific, 2008, 35–56 | MR | Zbl
[26] Bokut L. A., Chen Y., Liu C., Gröbner–Shirshov bases for dialgebras, arxiv: 0804.0638[math.RA]
[27] Bokut L. A., Chen Y., Qiu J., Gröbner–Shirshov bases for associative algebras with multiple operators and free Rota–Baxter algebras, arxiv: 0805.0640[math.RA] | MR
[28] Bokut L., Chen Y., Zhao X., “Gröbner–Shirshov beses for free inverse semigroups”, Internat. J. Algebra Comput., 19:2 (2009), 129–143 ; arxiv: 0804.0959[math.GR] | DOI | MR | Zbl
[29] Bokut L. A., Chibrikov E., “Lyndon–Shirshov words, Gröbner–Shirshov bases, and free Lie algebras”, Non-Associative Algebra and Its Applications, Lect. Notes Pure Appl. Math., 246, eds. L. V. Sabinin, L. Sbitneva, I. P. Shestakov, CRC Press, 2006, 17–34 | MR
[30] Bokut L. A., Fong Y., Ke W.-F., “Composition diamond lemma for associative conformal algebras”, J. Algebra, 272 (2004), 739–774 | DOI | MR | Zbl
[31] Bokut L. A., Fong Y., Ke W.-F., Shiao L.-S., “Gröbner–Shirshov bases for the braid semigroup”, Proc. of the ICM Satellite Conf. in Algebra and Related Topics (Hong Kong, China, August 14–17, 2002), World Scientific, River Edge, 2003, 60–72 | MR | Zbl
[32] Bokut L. A., Kang S.-J., Lee K.-H., Malcolmson P., “Gröbner–Shirshov bases for Lie supalgebras and their universival enveloping algebras”, J. Algebra, 217:2 (1999), 461–495 | DOI | MR | Zbl
[33] Bokut L. A., Kolesnikov P. S., “Gröbner–Shirshov bases: Conformal algebras and pseudoalgebras”, J. Math. Sci., 131:5 (2005), 5962–6003 | DOI | MR | Zbl
[34] Bokut L. A., Kukin G. P., Algorithmic and combinatorial algebra, Math. Its Appl., 255, Kluwer Academic, Dordrecht, 1994 | MR | Zbl
[35] Bokut L. A., Shiao L.-S., “Gröbner–Shirshov bases for Coxeter groups”, Commun. Algebra, 29:9 (2001), 4305–4319 | DOI | MR | Zbl
[36] Buchberger B., Ein Algorithmus zum Auffinden der Basiselemente des Restklassenringes nach einem nulldimensionalem Polynomideal, Dissertation, Univ. of Innsbruck, 1965
[37] Buchberger B., “Ein algorithmisches Kriterium für die Lösbarkeit eines algebraischen Gleichungssystems”, Aequationes Math., 4 (1970), 374–383 | DOI | MR | Zbl
[38] Burde D., “Left-symmetric algebras, or pre-Lie algebras in geometry and physics”, Central European J. Math., 4:3 (2006), 323–357 | DOI | MR | Zbl
[39] Cayley A., “On the theory of analytic forms called trees”, Collected Mathematical Papers, 3, Cambridge Univ. Press, Cambridge, 1980, 242–246
[40] Chen K.-T., Fox R. H., Lyndon R. C., “Free differential caculus. IV. The quotient groups of the lower central series”, Ann. Math., 68 (1958), 81–95 | DOI | MR | Zbl
[41] Cohn P. M., Universal Algebra, Harper Row, New York, 1965 | MR | Zbl
[42] Drensky V., Holtkamp R., Planar trees, free nonassociative algebras, invariants, and elliptic integrals, , 2008 arxiv: 0710.0493v2[math.RA] | MR
[43] Ebrahimi-Fard K., Guo L., “Free Rota–Baxter algebras and rooted trees”, J. Algebra Appl., 7 (2008), 167–194 | DOI | MR | Zbl
[44] Gerstenhaber M., “The cohomology structure of an associative ring”, Ann. Math., 78 (1963), 267–288 | DOI | MR | Zbl
[45] Hironaka H., “Resolution of singulatities of an algebtaic variety over a field if characteristic zero. I”, Ann. Math., 79 (1964), 109–203 ; “II”, 205–326 | DOI | MR | Zbl
[46] Kang S.-J., Lee K.-H., “Gröbner–Shirshov bases for irreducible $\mathrm{sl}_{n+1}$-modules”, J. Algebra, 232 (2000), 1–20 | DOI | MR | Zbl
[47] Kang S.-J., Lee K.-H., “Gröbner–Shirshov bases for representation theory”, J. Korean Math. Soc., 37 (2000), 55–72 | MR | Zbl
[48] Kang S.-J., Lee I.-S., Lee K.-H., Oh H., “Hecke algebras, Specht modules and Gröbner–Shirshov bases”, J. Algebra, 252 (2002), 258–292 | DOI | MR | Zbl
[49] Kang S.-J., Lee D.-I., Lee K.-H., Park H., “Linear algebraic approach to Gröbner–Shirshov basis theory”, J. Algebra, 313 (2007), 988–1004 | DOI | MR | Zbl
[50] Koszul J.-L., “Domaines bornés homogènes et orbites de groupes de transformations affines”, Bull. Soc. Math. France, 89 (1961), 515–533 | MR | Zbl
[51] Kozybaev D., Makar-Limanov L., Umirbaev U., “The Freiheitssatz and autoumorphisms of free right-symmetric algebras”, Asian-European J. Math., 1:2 (2008), 243–254 | DOI | MR | Zbl
[52] Latyshev V. N., “A combinatorial complexity of Gröbner bases”, J. Math. Sci., 102:3 (2000), 4134–4138 | DOI | MR | Zbl
[53] Latyshev V. N., “An improved version of standard bases”, Formal Power Series and Algebraic Combinatorics, Proc. of the 12th Int. Conf., FPSAC' 00 (Moscow, Russia, June 26–30, 2000), ed. D. Krob, Springer, Berlin, 2000, 496–505 | MR | Zbl
[54] Latyshev V. N., “Canonization and standard bases on filtered structures”, Lie Algebras, Rings and Related Topics, Papers of the 2nd Tainan–Moscow International Algebra Workshop' 97 (Tainan, Taiwan, January 11–17, 1997), ed. Y. Fong, Springer, Hong Kong, 2000, 61–79 | MR | Zbl
[55] Latyshev V. N., “A general version of standard basis and its application to T-ideals”, Acta Appl. Math., 85:1–3 (2005), 219–223 | DOI | MR | Zbl
[56] Lyndon R. C., “On Burnside problem”, Trans. Amer. Math. Soc., 77 (1954), 202–215 | DOI | MR | Zbl
[57] Mikhalev A. A., Zolotykh A. A., Combinatorial Aspects of Lie Superalgebras, CRC Press, Boca Raton, 1995 | MR | Zbl
[58] Reutenauer C., Free Lie Algebras, Oxford Univ. Press, Oxford, 1993 | MR | Zbl
[59] Segal D., “Free left-symmetric algebras and an analogue of the Poincaré–Birkhoff–Witt theorem”, J. Algebra, 164 (1994), 750–772 | DOI | MR | Zbl
[60] Ufnarovskij V. A., “Combinatorial and asymptotic methods in algebra”, Algebra VI: Combinatorial and Asymptotic Methods of Algebra: Non-Associative Structures, Encycl. Math. Sci., 57, eds. A. I. Kostrikin, I. R. Shafrevich, Birkhäuser, Berlin, 1995 | MR
[61] Viennot G., Algèbres de Lie Libres et Monoides Libres, Lect. Notes Math., 691, Springer, Berlin, 1978 | MR | Zbl